Question

Typically in natural language we will say something like 'I have two' to denote a group of two things, obviously using the 'mathematical' view of numbers as an abstract object with well defined 'names' that denote them. Being abstract in nature it is impossible for any person to 'have it'.

Do we draw any meaningful ontological distinction between number as used in mathematics and as used casually in natural language settings? For example 'one' can be used as an indefinite description like 'one thing', or simply imprecise language, talking this way is so widespread in everyday situations.

Answer 1

The ontological distinction between numbers in mathematics and in natural language settings lies in the precision and abstract nature of mathematical numbers compared to their more flexible and imprecise use in everyday language.

In natural language, the use of numbers is often more flexible and imprecise compared to their use in mathematics.

In everyday situations, we may use numbers as indefinite descriptions or in imprecise language. However, in mathematics, numbers are seen as abstract objects with well-defined properties.

While there may be some overlap in the use of numbers in natural language and mathematics, the ontological distinction lies in the precision and abstraction of mathematical numbers.

For example, when we say 'I have two,' we are using 'two' as a general descriptor without specifying the exact quantity. In mathematics, 'two' represents a specific quantity and follows defined rules of addition and multiplication.

Overall, the meaningful ontological distinction between numbers in mathematics and in natural language settings lies in the precision and abstract nature of mathematical numbers compared to their more flexible and imprecise use in everyday language.